Physical modeling of resonance phenomena in the long wave dynamics

Nizar Abcha,Alexander Ezersky,Efim Pelinovsky

doi:10.1051/lhb/2016008

Abstract

We have prepared two sets of experiments in a wave flume to model effects occurring in nature and to demonstrate resonance phenomena in laboratory conditions. The first set was performed to investigate non-linear wave run-up on the beach caused by harmonic wave maker located at some distance from the shore line. It is revealed that under certain wave excitation frequencies a significant increase in run-up amplification is observed [Ezersky et al. 2013]. It is found that this amplification is due to the excitation of resonant mode in the region between the shoreline and wave maker. Frequency and magnitude of the maximum amplification are in good correlation with the numerical calculation results represented in the recently published paper [Stefanakis et al. 2011]. The second set of experiments was performed to study resonance effects due to parametric excitation of edge waves. It is known that surface waves propagating toward the shore can excite edge waves propagating along the shore line. Although the edge wave amplitude decreases in an offshore direction they may contain enough energy to be responsible for erosion of the shore and generate so-called cusps [Buchan et al. 1995]. We investigate parametric mechanism of such generation when plane surface wave with frequency W excite edge wave with frequency W/2. It is show that parametric generation of edge waves can amplify run-up up to two times.

Highlights

The resonance phenomena plays significant role in the amplification of the long surface waves, especially tsunami waves, in coastal areas leading to the long‐time weakly damped water oscillations, late approach of a maximal amplitude wave comparing with leading waves, grouping structure of tsunami waves
Analysis of tsunami records showed that reflections due to bottom topography may result in appearance of resonant mode in coastal zone, see for instance Neetu et al [2011]
Results pre‐ sented in fig. 2 were obtained for force‐controlled regime of wave maker; the same results for coefficient of run‐up amplification were obtained for displacement control regime

Summary

INTRODUCTION

The resonance phenomena plays significant role in the amplification of the long surface waves, especially tsunami waves, in coastal areas leading to the long‐time weakly damped water oscillations, late approach of a maximal amplitude wave comparing with leading waves, grouping structure of tsunami waves. The maxi‐ mal run‐up height can be 50 times greater than the free surface oscillation amplitude used as the boundary condi‐ tions in the numerical calculations It was established in [Stefanakis et al 2011] that the wave period for which maximal run‐up amplification is observed depends on the slope of the bottom and the depth of water in the place where the waves are excited. This mechanism is connected with parametric excitation of standing edge wave with frequency w/2 by surface wave with frequency w propagating per‐ pendicular a shore line Such mechanism was investigated theoretically [Blondeaux et al 1995; Guza et al 1974] and it was identified in marine experiments in coastal zone [Huntley et al 1978].

EXPERIMENTAL SETUP

III.1. Resonance phenomena

III.2. Parametric excitation of edge waves

IV.1. R esonance phenomena

IV.2. P arametric excitation of edge waves

C ONCLUSIONS